Let f = {(1,1), (2,3),(0, -1), (- 1, - 3)} be a function from Z to Z defined by `f (x) = ax + b`, for some integers a,b. determine a,b.

Let f={(1,1),(2,3),(0,-1),(-1,-3)} be a linear function from Z into Z . Find f(x) .

Let f = {(1,1),(2,8),(3,27),(4,64),} be a function write a formula for f (x)

Show that the function f:RtoR defined by f(x)=2x-3 is one-one and onto. Find f^-1

Let A = {1, 2, 3}, B { 4, 5, 6} and let f = {(1,4),(2,5)(3,6)} be a function from A to B. Show that f is one-one.

Let A = {x,y,z) and B = {1,2}. Find the number of relations from A to B

Let A = R -{3} , B = R - {1} and let f: A rarr B be defined by f(x) = (x-2)/(x-3) . Check the nature of function.

Let A = R - {-3} and B = R - {1} Consider the function f : A rarr B defined by f(x) = (x-2)/(x-3) . Is f one-one and onto ? Justify your answer.

Let A={-1,0,1,2,} B={-4,-2,0,2} and f, g: A rarr B be functions defined by f(x)=x^2-x, x in A and g(x)=2|x-1/2|-1, x in A .Are f and g equal?. Justify your answer.

Consider the set A={1,2,3,4,5} , and B={1,4,9,16,25} and a function f:AtoB defined by f(1)=1 , f(2)=4 , f(3)=9 , f(4)=16 and f(5)=25 . Does f^-1 exists? Explain.